LONG WAVE RADIATION AT SEA SURFACE

1
LONG WAVE RADIATION AT SEA SURFACE
The long wave radiation is the radiation emitted
by the ocean surface at wavelengths greater than
those of the visible light (at about 800
nanometres (nm)) but shorter than those of
microwaves (at about 800,000 nm). Infrared
radiation is associated with heat energy and not
with visible light.
We will consider the NET long wave (LWnet??)
radiation at sea surface which represents the
difference between the upward infrared radiation
emitted by the ocean surface (LWs?) and downward
infrared radiation from the atmosphere
(LWa?) LWnet?? LWs? - LWa?
(1)
2
Net LW radiation at sea surface comes out as a
result of many complex processes
LWnet?????
3
The ocean surface irradiance consists of the
emitted LW radiation from the sea surface and
reflected atmospheric LW irradiance LWs?
LWs0? ?LLWa?
(2) where LWs0? is LW irradiance of ocean
surface ?L is surface long wave
albedo Thus, the net LW radiation at sea surface
can be expressed as LWnet?? LWs0? -
(1-?L)LWa? (3)
4
Two industrial workers go for a lunch

• They take (besides the meals) each cup of tea
  simultaneously.
• The first worker puts sugar into the cup
  immediately and starts to eat the
• main dish.
• The second worker first starts to eat and puts
  the sugar into the cup just
• before the drinking.

They start to drink their tea simultaneously
Whose tea will be hotter at the moment of
drinking?


5
Upward long wave irradiance from sea
surface This is the major component of longwave
exitance!!!! For this part the physics is a
simple blackbody radiation LWs0? ??Ts4
(4) where ?
is the Stefan-Boltzmann constant
(5.67?10-8?W?m-2?K-4) Ts is the
sea surface !!!skin!!! temperature in degrees
Kelvin ? is the
emissivity of the sea surface Emissivity of the
sea surface ? in a general case depends on the
sea state and optical properties of the sea
water. For the fresh water ? 0.92 and varies
from 0.89 to 0.98 for different conditions.
6
Sea surface skin temperature Ts is not equivalent
to SST, measured at ships by buckets or engine
intakes, it is the temperature of very thin
(several to several hundreds ?) surface skin
layer, namely skin temperature. Longwave
absorption and emission both take place in just
about the top 0.5 mm of water, depending on
wavelength. Back to the skin temperature issue
- later
Downward amospheric long wave irradiance Downwell
ing longwave radiation (longwave irradiance)
originates from the emission by atmospheric gases
(mainly water vapor, carbon dioxide and ozone),
aerosols and clouds. Long-wave albedo is also
poorly known and depends on the sea state and
cloud conditions. Downwelling LW is the smallest,
but the most uncertain term in the net LW
radiation (longwave exitance).
7
Determining surface net long wave radiation
Measurements
Modelling - RTMs
Parameterization
8
Measurements of LW radiation
The pyrgeometer is of a similar construction to
the pyranometer, but the single dome is made from
silicon or similar material transparent to the
longwave band, coated on the inside with an
interference filter to block shortwave radiation.
The longwave irradiance passing through the dome,
which we wish to determine, is only one component
of the thermal balance of the thermopile. The
remaining components come from various parts of
the instrument. To isolate the geophysical
component, the manufacturers provide the
correction equations.
9
More detailed description of pyrgeometer
The PIR, or pyrgeometer, is sensitive to
wavelengths in the range from 3000 to 50000 nm,
which covers the span of temperatures (or thermal
radiation) expected from the earth and
atmosphere. The pyrgeometer works on the same
principle as the pyranometer in that radiant
energy is converted to heat energy which, in
turn, is measured by a thermopile. However,
protecting the sensor from the environment (e.
g., solar radiation) is difficult. To do this,
the dome is made of silicon, which is nearly
opaque to solar wavelengths. The dome is also
coated with a grayish interference filter that
does not transmit wavelengths shorter than 3000
nm, but sharply increases to 50 transmission at
4000 nm. From 4000 to 50000 nm its transmittance
slowly falls to about 30-40. The detector senses
a net signal from a number of sources which
includes emissions from targets in its field of
view, emission from the case of the instrument,
and emission from the dome. To resurrect the true
environmental thermal infrared irradiance,
temperatures of the detector, case, and dome are
monitored with thermistors. Because the case is
shielded from the sun, its temperature represents
the air temperature and therefore is a proxy for
the degree of thermal emission by the atmosphere.
The dome, however, is not protected from solar
heating. Therefore, the difference between the
thermal emissions of the case and dome represents
an erroneous signal that must be removed. (As
mentioned before, shading the dome would make
this error negligible.) An empirical calibration
equation accounts for all of these effects and
converts the three measured temperatures to a
true environmental thermal infrared irradiance in
watts per square meter.
Requirements for calibration facilities
Calibrating facilities for infrared instruments
are more complicated and therefore less common
than those for solar radiation, and require
careful technique. Field intercomparisons if
several instruments are available are desirable.
The use of on-site atmospheric soundings in
clear-sky conditions can provide an absolute
reference for longwave irradiance. The
calculation of the downwelling longwave flux
under a cloud requires knowledge of both cloud
base height and emissivity. Cloud base height may
be measured with active systems such as a
MicroPulse lidar (Spinhirne, 1993) or a cloud
profiling radar, although an infrared radiometer
(such as the pyrgeometer) would still be needed
to estimate cloud emissivity.
10
Modelling of the long wave radiation (RTMs) The
radiative transfer equation (RTE) states that the
energy radiated by a parcel of material in a
particular frequency range and particular
direction (denoted by an increment of solid angle
around the direction) is the sum of energy
transmitted through the parcel and the energy
emitted from within the parcel, in that frequency
interval and direction. RTE evaluates the
effect of changes in temperature, humidity,
cloud, aerosols, and chemical composition.
Calculation of LW radiation should include all
the major absorption bands of CO2, H2O, and O3,
as well the weaker bands of CO2, N2O and CH4.
Structure of a simple RTM
Atmospheric column consists of N plane parallel
layers, n1,2,,N. Temperatures Tn, n0,1,.,N
are denoted at layer edges. The mean optical
thickness of the nth layer at a particular
frequency ? is ??n.
11
At frequency ? and beam angle ? the upward IR
irradiance U?,n and the downward IR irradiance
D?,n at the edges of the layer n are

(5.6)
where ? cos?. In (5,6) the first terms are the
transmitted IR irradiances given by Lamberts
law, and the second terms are the IR irradiances
emitted in the layer
(7,8)
where B?,n is the Planck function at frequency ?
and temperature Tn. Boundary conditions
(9,10)
?? is the albedo, ??1-?? is the emissivity of
the ocean surface. Equation (9) no downward IR
flux at the top of the atmosphere. Equation
(10) the upflux at the ocean surface is given by
the sum of emission from the ocean plus the
reflection of the downward flux.
12
For the frequency range ?a,?b the total upward
Un and downward Dn IR fluxes result from
integrating U?,n and U?,n overall frequencies in
?a,?b and beam angles
9,10

• Problems
• Numerical solution of (5)-(12) is difficult and
  expensive due to
• The spectral complexity of the atmospheric
  constituents
• Vertical inhomogeneity of the chemical
  composition of the
• atmosphere
• There is a lack of measurements of basic
  parameters in the atmospheric column

13
Short summary
Most exact are the Line-By-Line Radiative
Transfer Models (LBLRTM) which compute transfer
of each constituent for each emission and
absorption spectral line at many levels
throughout the profile. Their computational
burden is therefore large, which makes them
unsuitable for routine use in numerical models.
Over the years therefore, many broadband RTM's
have been developed, increasing in accuracy and
efficiency with improved parameterizations and
increased computer power. Such models are widely
applied in climate modelling, and in flux
retrieval from direct and remotely sensed
atmospheric variables. The computation of LW
flux with the best high spectral resolution codes
under clear conditions is at an advanced
state. For cloudy sky conditions, however, RTM's
are not well validated. The calculation of the
downwelling longwave flux under a cloud requires
knowledge of both cloud base height and
emissivity.
14
Parameterization of LW radiation
LWnet?? LWs0? - (1-?L)LWa?
What do we measure? SST
Ta, q, C (Cn, Cl)
1. No problem to parameterize the LWs0? , if we
have SST and the emissivity of the sea
surface LWs0? ??Ts4 However, you have to
remember that is Ts4 a skin temperature and is
not equal to the bulk SST (LATER!)
15

• 2. LW albedo is more poorly known that a SW
  albedo. Some very tentative estimates give values
  in the range of 0.04-0.05 (e.g. Clark et al.
  1974). Since
• the value 1-LW albedo is close (at least of
  the same
• order as) to the emmissivity of sea surface
  ?
• the accuracy of ?L and ? is approximately the
  same
• there is an approach to establish an effective
  emissivity and to re-write the equation for the
  net LW as follows

LWnet?? ??Ts4 ? - (1-?L)LWa?
LWnet?? ?(?Ts4 ? - LWa?)
(13)
where ? is an effective emissivity and should not
be understood as an emissivity of the sea surface
(typical mistake). From (2), (4), (13)
? (LWs0? - LWa?)/ (?Ts4 ? - LWa?)
(14)
Important
? ? ? LWs0? / ?Ts4 ?
16
3. Parameterization of downwelling atmospheric LW
radiation
LWnet?? ? (?Ts4? - LWa? )
The simplest approach is to measure downwelling
LW radiation and to compare it with different
combinations of surface parameters
Tair, q, Cn, Cl
However, this approach results in very uncertain
dependencies due to very different optical
properties of clear sky and cloudy atmosphere.
Air temperature blackbody radiation shows
significant differences for clear skies and
cloudy skies.
17
Guest (1998) 2 months of direct LW
measurements in Weddell Sea
Cloudy conditions
Clear sky
Processes are quite different under clear skies
and clouds
! separate analysis should be performed for
atmospheric LW under clear sky and clouds
18

• 1. Downwelling long wave radiation under clear
  skies
• Since information about atmospheric gases and
  aerosols is generally unavailable in routine
  observational practice, major efforts of
  researchers were concentrated on studying
  relationships between the clear sky downwelling
  atmospheric LW on
• Surface humidity
• Surface air temperature
• Theoretically, from a physical view point,
  surface humidity should have a closer link with
  surface humidity.

Bignami et al. (1995) using results from direct
observations in seven cruises in Mediterranean
Sea, found close relationship between surface
water vapor pressure and the ratio between
atmospheric downwelling LW and air temperature
blackbody radiation LWa? ?Ta4(abe?) where
a0.684, b0.0056, ?0.75

19

• However, in practice much better relationships
  are observed for surface air temperature.
  Reasons
• more easily available (more observations)
• measurements are more accurate
• Swinbank (1963) from Indian Ocean and lake
  observations

LWa? ?Ta4(abTa?)
(14a) or
ln(LWa? / ?Ta4) a?ln(Ta)
(14b) where a-15.75,
?0.75
Guest (1998) tested many formulations of clear
sky atmospheric LW. ? No evidence of a better
approximation for humidity than for air
temperature.
20
Guest (1998) results (for your files)
21
Malevsky et al (1992) from a very big data set
collected in different World Ocean regions (incl.
tropics and mid-latitudes) found the following
relationship between the downwelling atmospheric
LW and humidity (water vapor pressure) LWa?
?Ta4(0.600.049?e)
(16) Similar dependency for air temperature
was LWa? 1.026Ta2?10-5 0.541
(17) There has been found considerably lesser
scatter for (17) than for (16) and a smaller RMS
error. INTERESTING equation (17) looks
physically less reasonable than those which
include ?Ta4. However, analysis of empirical
data shows that formula (17) works well in most
conditions.
22
Thus, now we assume the following form of
parameterization of the net LW radiation
Sea surface !skin! temperature blackbody
radiation. Since we do not have normally skin
estimate, we account for the bulk effect in ?
Effective emissivity of sea surface (accounts for
the LW albedo and skin effect) ? ?!!!

LWnet?? ? ?Ts4? - ( LWa0? ? F(c) )
?
Atmospheric downwelling LW under clear
skies Parameterized as a function of either
surface humidity or surface temperature Relations
hips with temperature give better results!
Function of cloud cover Should account for the
effect of clouds
23
2. Downwelling long wave radiation under clouds
the cloud modification of LWa?. What should be
parameterized from a theoretical view point is a
cloud temperature blackbody radiation ?Tcl4?
Lind and Katsaros (1982)
LWc?(2) n(2)?(2) ?Tcl(2)4 1-n(2) LWc?(3)
LWc?(1) n(1)?(1) ?Tcl(1)4 1-n(1) LWc?(2)
LWc?(tot) (1-?(0)) LWc?(1)
LWa?(sky) ?(0)?T0(1)4

• n is fractional cloud cover of the
• subscribed cloud layer
• Tcl is cloud base temperature of the
• subscribed cloud layer
• ? is effective emittance of the
• subscribed cloud layer
• ?(0) is emittance of layer from the surface
• to lowest cloud base
• Tcl is equivalent radiative temperature of
• the lower layer

We DO NOT know (measure)
We come actually to another RTM!

24
The only available parameter is the total
fractional cloud cover and sometimes is the
fractional cover of the low-level
cloudiness. Typical approach to make
measurements under the known cloud conditions
and to compare clear sky atmospheric LW with
that measured under the cloudy sky.
Paramete- rization of F(n)

Bignami et al. (1995) F(n) 10.1762c2
(Mediterranean Sea) Clark et al. (1974)
F(n) 1-0.69c2 (Pacific Ocean) Efimova
(1962) F(n) 1-0.80c (land data)

Typical expression is 1?ac? for the total
cloud cover
This effect has to be parameterized
25
Malevsky et al. (1992) from his collection of
field measurements for the total cloud cover
found LWcla? 0.928Ta2?10-5 0.397
(18) He assumed that LWcla? LWa?
(1ktnt2)
(19) Coefficient kt can be derived from (19)
under nt1 kt (LWcla? LWa?) / (LWa?)
(20) where LWa?
1.026Ta2?10-5 0.541) Not surprisingly, in this
formulation kt becomes dependent on the air
temperature, since both LWcla? and LWa? are the
functions of air temperature.
26
Computation of the kt from a simple RTM kt
(1/LWa?) ?cl?a Tcl4
LWa?(0)(4?h/Ta)-1



?cl emissivity of the cloud base
?cl
temperature of the cloud base
LWa?(0)
irradiance below the cloud layer
?cl surface
temperature ? - temperature gradient in the
undercloud layer h cloud layer height
Thus, for the total cloud cover only
LWa? LWa0? ? F(c)(1.026Ta210-5-0.541)(1ktnt2
) kt (-0.098Ta2?10-5 0.144) /
(1.026Ta210-5-0.541)
27
Malevsky et al. (1992) first considered the
effect of cloudiness for three different layers
(low cloudiness, mid-level cloudiness and upper
layer cloudiness).
For upper layer LWclua? 0.995Ta2?10-5
0.496 (21) For mid-level
LWclma? 0.932Ta2?10-5 0.401 (22) For
lower layer LWclla? 0.921Ta2?10-5
0.385 (23)
For the cloud coefficients
For upper layer ku (LWclua?LWa?)/(LWa?)
(24) For mid-level km
(LWclma?LWa?)/(LWa?) (25) For lower
layer kl (LWclla?LWa?)/(LWa?)
(26)
28
However, normally we have observations only for
the fractional cloud cover of total and
low-layer cloudiness. Thus, this 3-layer
formulation has been simplified for the
consideration of the total and low-layer
cloudiness
LWa? (1.026Ta210-5-0.541)(1klnl2)(1kum(nt2-nl
2) (27)
kum is the coeeficient accounting for the total
effect of the mid and upper layer cloudiness,
which can be derived from the coefficients for
the total and low-level cloudiness
kl (LWclla?LWa?)/(LWa?)
(28) kum (ktnt2 - klnl2) /
(1ktnt2)(nt2nl2) (29)
Now we can finally derive the parameterization of
the net long-wave radiation at ocean surface in a
general form
LWnet?? ? ?Ts4? - (LWa0? ? F(c))
29

• Summary
• History is very long
• The number of parameterizations approaches
  several tens
• Formulations are similar
• Differences are large

Brunt (1932) LW??Ts4(0.39-0.05ez1/2)(1-0.8nd), ?0.98, d1
Berliand and Berliand (1952) LW??Ts4(0.39-0.05ez1/2)(1-0.8nd)4??Ta3(Ts-Ta), ?0.98, d1
Anderson (1952) LW??Ts4-Ta4(0.740.0049ez)(1-0.8 nd), ?0.98, d1
Efimova (1961) LW??Ta4(0.254-0.00495ez)(1-cnd)4??Ta3(Ts-Ta), ?0.96, d1
Swinbank (1963) LW??Ts4-9.36?10-6Ta6(1-0.8 nd), ?0.98, d1
Clark et al. (1974) LW??Ts4(0.39-0.05ez1/2)(1-cnd)4??Ta3(Ts-Ta), ?0.98, d2
Bunker (1976) LW0.022??Ta4(11.7-0.23ez)(1-0.68nd)4??Ta3(Ts-Ta), ?0.96, d1
Hastenrath and Lamb (1978) LW??Ts4(0.39-0.056q1/2)(1-0.53nd)4??Ta3(Ts-Ta), ?0.98, d2
Malevsky et al. (1992b) LW?(?Ts4-(1.026Ta210-5-0.541)(1cnd)), ?0.91, d2
Bignami et al. (1995) LW??Ts4-?Ta4 (0.6530.00535 ez)(10.1762nd)), ?0.98, d2
Josey et al. (2001) LW??Ts4-(1-?L)?Ta an2 bn c 0.84(D4.01)4 , ?0.98, a, b, c, D empirical coefficients, ?L 0.045
30
Variations in short-wave radiation and long-wave
radiation due to the parameterizations (North
Atlnatic SW and LW radiation budget)
31

• Summary of LW radiation parameterizations
• Under clear sky and small cloudiness the
  accuracy is
• normally better than 15 W/m2
• Higher uncertainties occur under the moderate
  and high
• cloud cover
• Uncertainties in the tropics are typically
  higher than in
• mid and high latitudes and are primarily
  associated with
• atmospheric clear sky IR irraidance
• Hot issues of all parameterizations are skin
  
• temperature and representation of the
  multi-layer
• cloudiness of different types by fractional
  total cloud
• cover

32

• Recommendations
• Do not hesitate to use old parameterizations
  
• Try to avoid the use of parameterizations
  based on water
• vapor pressure and humidity
• Do not use Bignami et al. (1995) except for
  Mediterranean
• sea
• Be careful with the choice of emissivity
  value. Always
• remember it is effective emissivity and
  not the
• emissivity of surface

33
Radiation balance of the ocean
RB SW?(1-?) - LWnet?? (30)
LW
SW
Winter Spring Summer Fall
34
SW
LW
RB
35
Variations of SW and LW radiation due to
different parameterizations
36

• /helios/u2/gulev/handout/
• longwave1.f collection of LW radiation F77
  codes
• RIZL Malevsky et al. (1992) scheme
• RLWISI Efimova (1961) as modified by Isemer et
  al (1989)
• RLW_CLA Clark et al. (1974)
• RLW_BIG Bignami et al. (1995)
• Try to compare Malevsky, Efimova, Bignami and
  Clark schemes
• For Ts 12C
• Clear sky, dependence on temperature, humidity
• Cloud cover octa4, dependence on temperature
• Tair 15C, dependence on cloud cover (in octas)

37

• /helios/u2/gulev/handout/
• swm_test.f program to compute instantaneous
  values of SW radiation, using Malevsky et al.
  (1992) and Dobson and Simth (1988) schemes.
• Compilation f77 o swm_test swm_test.f
  radiation.f
• Results sw.res
• swr_test.f program to compute daily values of
  SW radiation, using Reed (1977) scheme.
• Compilation f77 o swr_test swr_test.f
  radiation1.f
• Results swr.res
• lw_test.f program to compute values of LW
  radiation, using Malevsky et al. (1992), Clark et
  al. (1974), Bignami et al. (1995) and Emivova
  (1962) schemes.
• Compilation f77 o lw_test lw_test.f
  longwave1.f
• Results lw.res

38
READING Angström, A.K., 1925 On the variation
of the atmospheric radiation. Gerlands. Beitr.
Geophys., 4, 21-145. Bignami, F., R.Santorelly,
M.E.Schiano, and S.Marullo, 1991 Net long-wave
radiation in the western Mediterranean Sea.
Poster session at the 20th General Assembly of
the International Union of Geodesy and
Geophysics, IAPSO, Wien, August 1991. Bignami,
F., S.Marullo, R.Santorelly, and M.E.Schiano,
1995 Long-wave radiation budget in the
Mediterranean Sea. J. Geophys. Res., 100,
2501-2514. Brunt, D., 1932 Notes on radiation in
the atmosphere. Quart. J. Roy. Met. Soc., 58,
389-420 Bunker, A., 1976 A computation of
surface energy flux and annual cycle over the
North Atlantic Ocean. Mon. Wea. Rew., 104,
1122-1140. Clark, N.E., L.Eber, R.M.Laurs,
J.A.Renner, and J.F.T.Saur, 1974 Heat exchange
between ocean and atmosphere in the eastern North
Pacific for 1961-71. NOAA Tech Rep. NMFS
SSFR-682, US Dept. of Commer., Washington DC, 108
pp. Efimova, N.A., 1961 On methods of
calculating monthly values of net long-wave
radiation. Meter. Hydr. 10, 28-33. Fung, I. Y.,
D.E.Harrison, and A. A. Lacis, 1984 On the
variability of the net long-wave radiation at the
ocean surface. Rev. Geophys., 22(2),
177-193. Gulev, S.K., 1995 Long-term variability
of sea-air heat transfer in the North Atlantic
Ocean. Int.J.Climatol., 15, 825-852. Isemer,
H.-J., J.Willebrand, and L.Hasse, 1989 Fine
adjustment of large-scale air-sea energy flux
parameterizations by direct estimates of ocean
heat transport. J.Climate, 2, 1163-1184. Josey,
S., E.C.Kent, and P.K.Taylor, 1999 New insights
into the ocean heat budget closure problem from
analysis of the SOC air-sea flux climatology. J.
Climate, 12, 2856-2880. Lind, R.J., K.B.Katsaros,
and M.Gube, 1984 Radiation budget components and
their parameterization in JASIN. Quart. J. Roy.
Meteor. Soc., 110, 1061-1071. Lindau, R., 2000
Climate Atlas of the Atlantic Ocean derived from
the Comprehensive Ocean-Atmosphere Data Set.
Springer-Verlag, Berlin, 488 pp. Malevsky, S.P.,
G.V.Girdiuk, and B.Egorov, 1992b Radiation
balance of the ocean surface. Hydrometizdat,
Leningrad, 148 pp. Oberhuber, J.M., 1988 An
Atlas based on the COADS data set the budgets of
heat, buoyancy and turbulent kinetic energy at
the surface of the global ocean. MPI fuer
Meteorologie report, No. 15, 19pp. Available
from Max-Plank-Institute fuer Meteorologie,
Bundesstrasse 55, Hamburg, Germany. Rosati, A.
and K. Miyakoda, 1988 A general circulation
model for the upper ocean circulation. J. Phys.
Oceanogr., 18, 1601-1626.